We present a model with leverage and margin constraints that vary across investors and time. We find evidence consistent with each of the model’s five central predictions: (1) Since constrained investors bid up high-beta assets, high beta is associated with low alpha, as we find empirically for U.S. equities, 20 international equity markets, Treasury bonds, corporate bonds, and futures; (2) A betting-against-beta (BAB) factor, which is long leveraged low- beta assets and short high-beta assets, produces significant positive risk-adjusted returns; (3) When funding constraints tighten, the return of the BAB factor is low; (4) Increased funding liquidity risk compresses betas toward one; (5) More constrained investors hold riskier assets.

Embedded Leverage

Many financial instruments are designed with embedded leverage such as options and leveraged exchange traded funds (ETFs). Embedded leverage alleviates investors’ leverage constraints and, therefore, we hypothesize that embedded leverage lowers required returns. Consistent with this hypothesis, we find that asset classes with embedded leverage offer low risk-adjusted returns and, in the cross-section, higher embedded leverage is associated with lower returns. A portfolio which is long low-embedded-leverage securities and short high-embedded-leverage securities earns large abnormal returns, with t-statistics of 8.6 for equity options, 6.3 for index options, and 2.5 for ETFs. We provide extensive robustness tests and discuss the broader implications of embedded leverage for financial economics.